WGCNA Exploratory Analysis

#setwd('/afs/inf.ed.ac.uk/user/s17/s1725186/Documents/PhD-Models/FirstPUModel/RMarkdowns')

library(tidyverse) ; library(reshape2) ; library(glue) ; library(plotly) ; library(dendextend)
library(RColorBrewer) ; library(viridis) ; require(gridExtra) ; library(GGally) ; library(ggpubr) ; library(ggExtra)
library(WGCNA)
library(expss)
library(polycor)
library(biomaRt)
library(clusterProfiler) # ORA
library(foreach) ; library(doParallel)

SFARI_colour_hue = function(r) {
  pal = c('#FF7631','#FFB100','#E8E328','#8CC83F','#62CCA6','#59B9C9','#b3b3b3','#808080','gray','#d9d9d9')[r]
}

Load preprocessed dataset (preprocessing code in01_data_preprocessing.Rmd) and clustering (pipeline in 05_WGCNA.Rmd)

# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
DE_info = DE_info %>% data.frame


# GO Neuronal annotations: regex 'neuron' in GO functional annotations and label the genes that make a match as neuronal
GO_annotations = read.csv('./../Data/genes_GO_annotations.csv')
GO_neuronal = GO_annotations %>% filter(grepl('neuron', go_term)) %>% 
              mutate('ID'=as.character(ensembl_gene_id)) %>% 
              dplyr::select(-ensembl_gene_id) %>% distinct(ID) %>%
              mutate('Neuronal'=1)


# SFARI Genes
SFARI_genes = read_csv('./../../../SFARI/Data/SFARI_genes_01-03-2020_w_ensembl_IDs.csv')
SFARI_genes = SFARI_genes[!duplicated(SFARI_genes$ID) & !is.na(SFARI_genes$ID),]


# Clusterings
clusterings = read_csv('./../Data/clusters.csv')


# Update DE_info with SFARI and Neuronal information
genes_info = DE_info %>% mutate('ID'=rownames(.)) %>% left_join(SFARI_genes, by='ID') %>% 
  mutate(`gene-score`=ifelse(is.na(`gene-score`), 'Others', `gene-score`)) %>%
  left_join(GO_neuronal, by='ID') %>% left_join(clusterings, by='ID') %>%
  mutate(Neuronal=ifelse(is.na(Neuronal), 0, Neuronal)) %>%
  mutate(gene.score=ifelse(`gene-score`=='Others' & Neuronal==1, 'Neuronal', `gene-score`), 
         significant=padj<0.05 & !is.na(padj))


rm(DE_info, GO_annotations, clusterings)

---

Dynamic Tree vs Dyamic Hybrid

Comparing module sizes

Dynamic Hybrid creates less and more balanced modules

plot_data = table(genes_info$DynamicTree) %>% data.frame %>% arrange(desc(Freq)) %>% filter(Var1 != 'gray')

p1 = plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + 
     geom_bar(stat='identity', fill=plot_data$Var1) + 
     geom_hline(yintercept = mean(plot_data$Freq), color = 'gray',linetype = 'dashed') +
     ggtitle('Modules using Dynamic Tree') + ylab('Number of genes') + xlab('Module') + 
     theme_minimal() + theme(axis.text.x = element_blank())

plot_data = table(genes_info$DynamicHybrid) %>% data.frame %>% arrange(desc(Freq)) %>% filter(Var1 != 'gray')

p2 = plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + 
     geom_bar(stat='identity', fill=plot_data$Var1) + 
     geom_hline(yintercept = mean(plot_data$Freq), color = 'gray',linetype = 'dashed') +
     ggtitle('Modules using Dynamic Hybrid') + ylab('Number of genes') + xlab('Module') + 
     theme_minimal() + theme(axis.text.x = element_blank())

grid.arrange(p1,p2, nrow=2, top = 'Comparison of Module sizes')

rm(p1, p2, plot_data)

Comparing genes left without a module

Dynamic Tree leaves 4230 genes without cluster (26%) Dynamic Hybrid leaves 138 genes without cluster (1%)

Dynamic Tree leaves many more genes without a cluster. As we saw in the dendrograms in 05_WGCNA.html, the genes usually left without a cluster are the ones closest to the root of the dendrogram, now we want to see if they share some characteristic in common: we suspect it may be a weak relation to ASD.

There seems to be a relation between DE and module membership, being DE a more restrictive condition than being assigned to a cluster

pca = datExpr %>% prcomp

plot_data = data.frame('ID'=rownames(datExpr), 'PC1' = pca$x[,1], 'PC2' = pca$x[,2]) %>%
            left_join(genes_info, by='ID') %>% mutate('hasCluster'=DynamicTree!='gray', 
                                                      'hasSFARIScore'=`gene-score`!='Others') %>%
            apply_labels(`gene-score`='SFARI Gene score', DynamicTree = 'Dynamic Tree Algorithm', 
                         significant = 'Differentially Expressed', hasCluster = 'Belongs to a Module',
                         hasSFARIScore = 'Has a SFARI Score', syndromic = 'Has syndromic tag')

p1 = plot_data %>% ggplot(aes(PC1, PC2, color=hasCluster)) + geom_point(alpha=0.2) + 
  theme_minimal() + ggtitle('Genes are assigned to a cluster') + theme(legend.position='bottom')

p2 = plot_data %>% ggplot(aes(PC1, PC2, color=significant)) + geom_point(alpha=0.2) + 
  theme_minimal() + ggtitle('Genes found to be DE') + theme(legend.position='bottom')

grid.arrange(p1, p2, nrow=1, top = 'Exploring unassigned genes using the Dynamic Tree algorithm')

rm(pca, p1, p2)

Most of the genes that don’t have a cluster are not differentially expressed:
98% of the genes that don’t have a cluster are not differentially expressed

cro(plot_data$significant, list(plot_data$hasCluster, total()))

	Belongs to a Module			#Total
	FALSE	TRUE
Differentially Expressed
FALSE	4151	7490		11641
TRUE	79	4412		4491
#Total cases	4230	11902		16132

Most of the genes with a SFARI score are assigned to a cluster:

138 of the SFARI genes (~17%) are not assigned to any cluster

cro(plot_data$hasSFARIScore, list(plot_data$hasCluster, total()))

	Belongs to a Module			#Total
	FALSE	TRUE
Has a SFARI Score
FALSE	4092	11251		15343
TRUE	138	651		789
#Total cases	4230	11902		16132

Conclusion:

The main difference between algorithms is that Dynamic Hybrid clusters outlier genes and Dynamic Tree leaves them out, so Dynamic Tree would give me a ‘cleaner’ group of genes to work with, without losing many SFARI genes, but Dynamic Hybrid has less and more balanced clusters

I think both options could be feasible, but I’m going to use the Dynamic Hybrid algorithm to keep more genes

clustering_selected = 'DynamicHybrid'
genes_info$Module = genes_info[,clustering_selected]

Dynamic Hybrid Modules

*The colour of the modules is the arbitrary one assigned during the WGCNA algorithm, where the gray cluster actually represents all the genes that were left without a cluster (so it’s not actually a cluster).

The Dynamic Hybrid algorithm created 55 modules and leaves 138 genes without a module

table(genes_info$Module)

## 
## #00A6FF #00ABFD #00B0F6 #00B4EF #00B7E7 #00B92F #00BADE #00BB48 #00BD5C #00BDD4 
##      39     299     157      58      32     225    1476     122     184      58 
## #00BE6E #00BECA #00BF7D #00C08C #00C0B3 #00C0BF #00C19A #00C1A7 #1FB700 #44A0FF 
##     142     301      99     155     381     331     431     423      32     550 
## #4BB400 #64B200 #6C9AFF #77AF00 #88AC00 #8993FF #96A900 #A08CFF #A3A500 #AEA200 
##     222      64     207    1239     900      30     168     233     181     214 
## #B385FF #B99E00 #C37EFF #C39A00 #CC9600 #D177FF #D49200 #DB8E00 #DD71FA #E28900 
##     163     174     710     305     295     597     244     123     344     365 
## #E76BF3 #E98428 #EE8045 #EF67EB #F47B5B #F663E2 #F8766D #FB61D8 #FB727D #FE61CD 
##     275     225     760      72     113     223      66      81      53      85 
## #FE6D8D #FF61C2 #FF63B6 #FF66A9 #FF699B    gray 
##     181     157     925     442      63     138

plot_data = table(genes_info$Module) %>% data.frame %>% arrange(desc(Freq))

ggplotly(plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + geom_bar(stat='identity', fill=plot_data$Var1) + 
         ggtitle('Module size') + ylab('Number of genes') + xlab('Module') + theme_minimal() + 
         theme(axis.text.x = element_text(angle = 90)))

Relation to external clinical traits

Quantifying module-trait associations

In the WGCNA documentation they use Pearson correlation to calculate correlations, I think all of their variables were continuous. Since I have categorical variables I’m going to use the hetcor function, that calculates Pearson, polyserial or polychoric correlations depending on the type of variables involved.

• I’m not sure how the corPvalueStudent function calculates the p-values and I cannot find any documentation…

• Compared correlations using Pearson correlation and with hetcor and they are very similar, but a bit more extreme with hetcor. The same thing happens with the p-values.

datTraits = datMeta %>% dplyr::select(Diagnosis, Region, Sex, Age, PMI, RNAExtractionBatch) %>%
            dplyr::rename('ExtractionBatch' = RNAExtractionBatch)

# Recalculate MEs with color labels
ME_object = datExpr %>% t %>% moduleEigengenes(colors = genes_info$Module)
MEs = orderMEs(ME_object$eigengenes)

# Calculate correlation between eigengenes and the traits and their p-values
moduleTraitCor = MEs %>% apply(2, function(x) hetcor(x, datTraits)$correlations[1,-1]) %>% t
rownames(moduleTraitCor) = colnames(MEs)
colnames(moduleTraitCor) = colnames(datTraits)
moduleTraitPvalue = corPvalueStudent(moduleTraitCor, nrow(datExpr))

# Create text matrix for the Heatmap
textMatrix = paste0(signif(moduleTraitCor, 2), ' (', signif(moduleTraitPvalue, 1), ')')
dim(textMatrix) = dim(moduleTraitCor)

# In case there are any NAs
if(sum(!complete.cases(moduleTraitCor))>0){
  print(paste0(sum(is.na(moduleTraitCor)),' correlation(s) could not be calculated')) 
}

rm(ME_object)

Modules have very strong correlations with Diagnosis with really small p-values and not much relation with anything else. Perhaps a little with PMI and Brain Region.

It’s a good sign that the gray module has a small correlation with diagnosis, since we know its composed mainly of not differentially expressed genes.

# Sort moduleTraitCor by Diagnosis
moduleTraitCor = moduleTraitCor[order(moduleTraitCor[,1], decreasing=TRUE),]
moduleTraitPvalue = moduleTraitPvalue[order(moduleTraitCor[,1], decreasing=TRUE),]

# Create text matrix for the Heatmap
textMatrix = paste0(signif(moduleTraitCor, 2), ' (', signif(moduleTraitPvalue, 1), ')')
dim(textMatrix) = dim(moduleTraitCor)


labeledHeatmap(Matrix = moduleTraitCor, xLabels = names(datTraits), yLabels =  gsub('ME','',rownames(moduleTraitCor)), 
               yColorWidth=0, colors = brewer.pal(11,'PiYG'), bg.lab.y = gsub('ME','',rownames(moduleTraitCor)),
               textMatrix = textMatrix, setStdMargins = FALSE, cex.text = 0.8, cex.lab.y = 0.75, zlim = c(-1,1),
               main = paste('Module-Trait relationships'))

diagnosis_cor = data.frame('Module' = gsub('ME','',rownames(moduleTraitCor)),
                           'MTcor' = moduleTraitCor[,'Diagnosis'],
                           'MTpval' = moduleTraitPvalue[,'Diagnosis'])

genes_info = genes_info %>% left_join(diagnosis_cor, by='Module')

rm(moduleTraitCor, moduleTraitPvalue, textMatrix, diagnosis_cor)

Modules with a high Module-Diagnosis (absolute) correlation should have a high content of differentially expressed genes:

This seems to be the case

plot_data = genes_info %>% group_by(Module, MTcor) %>% summarise(p = 100*mean(significant))

plot_data %>% ggplot(aes(MTcor, p)) + geom_hline(yintercept=mean(plot_data$p),color='gray',linetype='dotted') +
              geom_point(color=plot_data$Module, alpha = 0.8, aes(id=Module)) + 
              geom_smooth(color='gray', se=FALSE) + theme_minimal() + 
              xlab('Module-Diagnosis correlation') + ylab('% of DE genes in Module')

Gene Significance and Module Membership

Gene significance: is the value between the correlation between the gene and the trait we are interested in. A positive gene significance means the gene is overexpressed and a negative value means its underexpressed. (The term ‘significance’ is not very acurate because it’s not actually measuring statistical significance, it’s just a correlation, but that’s how they call it in WGCNA…)

Module Membership is the correlation of the module’s eigengene and the expression profile of a gene. The higher the Module Membership, the more similar the gene is to the genes that constitute the module. (I won’t use this measure yet)

Note: Some correlations weren’t able to be calculated with the original function (weirdly because the correlation was too strong), so they are calculated again in the end using the polyserial function instead of hetcor, which is robust enough to calculate them

# It's more efficient to iterate the correlations one by one, otherwise it calculates correlations between the eigengenes and also between the genes, which we don't need

# Check if MM information already exists and if not, calculate it
if(file.exists(paste0('./../Data/dataset_', clustering_selected, '.csv'))){
  
  dataset = read.csv(paste0('./../Data/dataset_', clustering_selected, '.csv'))
  dataset$Module = dataset[,clustering_selected]
  
} else {
  
  ############# 1. Calculate Gene Significance
  GS_info = data.frame('ID'=rownames(datExpr),
                       'GS'=datExpr %>% apply(1, function(x) hetcor(x,datMeta$Diagnosis)$correlations[1,2])) %>%
            mutate('GSpval'=corPvalueStudent(GS, ncol(datExpr)))
  
  #############  2. Calculate Module Membership
  
  #setup parallel backend to use many processors
  cores = detectCores()
  cl = makeCluster(cores-1)
  registerDoParallel(cl)
  
  # Create matrix with MM by gene
  MM = foreach(i=1:nrow(datExpr), .combine=rbind) %dopar% {
    library(polycor)
    tempMatrix = apply(MEs, 2, function(x) hetcor(as.numeric(datExpr[i,]), x)$correlations[1,2])
    tempMatrix
  }
  
  # Stop clusters
  stopCluster(cl)
  
  rownames(MM) = rownames(datExpr)
  colnames(MM) = paste0('MM',gsub('ME','',colnames(MEs)))
  
  # Calculate p-values
  MMpval = MM %>% corPvalueStudent(ncol(datExpr)) %>% as.data.frame
  colnames(MMpval) = paste0('MMpval', gsub('ME','',colnames(MEs)))
  
  MM = MM %>% as.data.frame %>% mutate(ID = rownames(.))
  MMpval = MMpval %>% as.data.frame %>% mutate(ID = rownames(.))
  
  # Join and save results
  dataset = genes_info %>% dplyr::select(ID, `gene-score`, clustering_selected, MTcor, MTpval) %>%
            left_join(GS_info, by='ID') %>%
            left_join(MM, by='ID') %>%
            left_join(MMpval, by='ID')
  
  write.csv(dataset, file = paste0('./../Data/dataset_', clustering_selected, '.csv'), row.names = FALSE)
  
  rm(cores, cl) 
  
}

GS_missing = dataset$ID[is.na(dataset$GS)] %>% as.character

if(length(GS_missing)>0){
  
  cat(paste0(length(GS_missing),' correlations between genes and Diagnosis could not be calculated, ',
             'calculating them with the polyserial function'))
  
  for(g in GS_missing){
    dataset$GS[dataset$ID == g] = polyserial(as.numeric(datExpr[g,]), datMeta$Diagnosis)
  }
  
}

## 2 correlations between genes and Diagnosis could not be calculated, calculating them with the polyserial function

## Warning in polyserial(as.numeric(datExpr[g, ]), datMeta$Diagnosis): initial
## correlation inadmissible, -1.0011728438261, set to -0.9999

## Warning in polyserial(as.numeric(datExpr[g, ]), datMeta$Diagnosis): initial
## correlation inadmissible, 1.00381117390601, set to 0.9999

rm(GS_missing)

Analysing concordance between these metrics in the genes

1. Gene Significance vs Log Fold Change

Gene significance and Log Fold Chance are two different ways to measure the same thing, so there should be a concordance between them

Log Fold Chance has a wider value range with outliers in the extremes, but both variables agree with each other quite well

plot_data = dataset %>% dplyr::select(ID, MTcor, GS) %>% 
            left_join(genes_info %>% dplyr::select(ID, gene.score), by='ID') %>%
            left_join(genes_info %>% dplyr::select(ID,baseMean,log2FoldChange,significant,Module), by='ID') %>%
            left_join(data.frame(MTcor=unique(dataset$MTcor)) %>% arrange(by=MTcor) %>% 
                                 mutate(order=1:length(unique(dataset$MTcor))), by='MTcor')

ggplotly(plot_data %>% ggplot(aes(GS, log2FoldChange)) +
         geom_point(color=plot_data$Module, alpha=0.5, aes(ID=Module)) + 
         geom_smooth(color='gray', se=FALSE) + theme_minimal() + xlab('Gene Significance') + 
         ggtitle(paste0('R^2 = ', round(cor(plot_data$log2FoldChange, plot_data$GS)[1]**2, 2))))

2. Module-Diagnosis correlation vs Gene Significance

In general, modules with the highest Module-Diagnosis correlation should have genes with high Gene Significance

Note: For the Module-Diagnosis plots, if you do boxplots, you lose the exact module-diagnosis correlation and you only keep the order, so I decided to compensate this downside with a second plot, where each point is plotted individually using their module’s Module-Diagnosis correlation as the x axis. I think the boxplot plot is easier to understand but the second plot contains more information, so I don’t know which one is better.

plot_data = plot_data %>% arrange(order)

ggplotly(plot_data %>% ggplot(aes(order, GS, group=order)) + geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('Gene Significance'))

## Warning: `group_by_()` is deprecated as of dplyr 0.7.0.
## Please use `group_by()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

plot_data %>% ggplot(aes(MTcor, GS)) + geom_hline(yintercept=0, color='gray', linetype='dotted') + 
         geom_point(color=plot_data$Module, alpha=0.1, aes(id=ID)) + geom_smooth(color='gray', se=FALSE) + 
         theme_minimal() + xlab('Module-Diagnosis correlation') + ylab('Gene Significance') + 
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, plot_data$GS)^2,2)))

3. Module-Diagnosis correlation vs Log Fold Change

The same happens with the Log Fold Change

ggplotly(plot_data %>% ggplot(aes(order, log2FoldChange, group=order)) + geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + 
         theme_minimal() + xlab('Modules ordered by Module-Diagnosis correlation') + ylab('log2FoldChange'))

ggplotly(plot_data %>% ggplot(aes(MTcor, log2FoldChange)) + 
         geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_point(color=plot_data$Module, alpha=0.1, aes(id=ID)) + geom_smooth(color='gray', se=FALSE) + 
         theme_minimal() + xlab('Module-Diagnosis correlation') + ylab('log2FoldChange') + 
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, plot_data$log2FoldChange)^2,2))))

4. Module-Diagnosis vs Mean Expression

In theory, there shouldn’t be a relation between module-diagnosis and mean expression, but in the the exploratory analysis, we saw that the overexpressed genes tended to have lower levels of expression than the overexpressed genes, and this pattern can be seen in these plots where the modules with negative Module-Diagonsis correlation have slightly higher levels of expression than the modules with positive Module-Diagnosis correlation, although this pattern is note very strong and all modules have similar levels of expression.

ggplotly(plot_data %>% ggplot(aes(order, log2(baseMean+1), group=order)) + 
         geom_hline(yintercept=mean(log2(plot_data$baseMean+1)), color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('log2(Mean Expression)'))

plot_data %>% ggplot(aes(MTcor, log2(baseMean+1))) + geom_point(alpha=.2, color=plot_data$Module, aes(id=ID)) + 
         geom_hline(yintercept=mean(log2(plot_data$baseMean+1)), color='gray', linetype='dotted') + 
         geom_smooth(color='gray', alpha=0.3) + theme_minimal() + 
         xlab('Module-Diagnosis correlation') + ylab('log2(Mean Expression)') +
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, log2(plot_data$baseMean+1))^2,2)))

Conclusion:

All of the variables seem to agree with each other, Modules with a high correlation with Diagnosis tend to have genes with high values of Log Fold Change as well as high values of Gene Significance, and the gray module, which groups all the genes that weren’t assigned to any cluster tends to have a very poor performance in all of the metrics.

---

SFARI Scores

Since SFARI scores genes depending on the strength of the evidence linking it to the development of autism, in theory, there should be some concordance between the metrics we have been studying above and these scores…

SFARI Scores vs Gene Significance

• All SFARI scores have a lower median than all genes that have a neuronal-related annotation (!)

• All SFARI scores have a higher median than the rest of the genes without a neuronal-related annotation

• Neuronal annotated genes have higher Gene Significance than genes without any neuronal-related annotation (makes sense)

• These differences are generally not statistically significant

comparisons = list(c('1','2'), c('2','3'), c('3','Neuronal'), c('Neuronal','Others'),
                   c('1','3'), c('3','Others'), c('2','Neuronal'),
                   c('1','Neuronal'), c('2','Others'), c('1','Others'))
increase = 0.06
base = 1.05
pos_y_comparisons = c(rep(base, 4), rep(base + increase, 2), base + 2:5*increase)

plot_data %>% ggplot(aes(gene.score, abs(GS), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .02) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:3,8,7))) + theme_minimal() + 
              ylab('Gene Significance Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Scores vs Module-Diagnosis correlation

• The higher the SFARI score, the lower the Module-Trait correlation (!)

• The group with the highest Module-Diagnosis correlation is SFARI score 3, which is supposed to be the one with the least amount of evidence suggesting a relation to autism (!)

• SFARI score 1 is the group with the lowest Module-Diagonsis correlation (!)

• Most differences are not statistically significant, but SFARI Score 1 does have a significant difference with all the other grous

increase = 0.05
base = 1
pos_y_comparisons = c(rep(base, 4), rep(base + increase, 2), base + 2:5*increase)

plot_data %>% ggplot(aes(gene.score, abs(MTcor), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:3,8,7))) + theme_minimal() + 
              ylab('Module-Diagnosis Correlation Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Enrichment vs Module-Diagnosis correlation

To study the strength of the relationship between a module and the biological signal found in the data related to ASD we have the Module-Diagnosis metric. We want to do a similar thing to calculate the ‘strength’ of the presence of SFARI Genes in each module to be able to identify the modules ‘enriched’ in SFARI Genes

The easiest metric would be to calculate the percentage of genes in each module that belong to the SFARI Genes, but this metric doesn’t take into account the size of the model and can favour more extreme but less robust results (small modules)

Instead, we are going to use the Over Representation Analysis (ORA) approach, that uses the hypergeometric distribution to calculate the probability of a module of size \(n\) containing at least \(k\) SFARI Genes and we are going to interpret this probability as the ‘enrichment’ of SFARI Genes in each module

Hypergeometric distribution explanation:

If we interpret the number of genes (\(n\)) in a cluster as \(n\) random draws without replacement from a finite population of size \(N\), and the number of SFARI genes in the cluster (\(s\)) as \(s\) successes in those \(n\) draws, where we know that \(N\) contains exactly \(S\) successes, then we can use the hypergeometric distribution to calculate the statistical significance of having drawn \(s\) successes out of \(n\) draws, and use this value to select the clusters with the highest statistical significance

Percentage of SFARI Genes vs ORA by Module

# Calculate % and ORA of SFARI Genes in each module

modules = unique(genes_info$Module[genes_info$Module!='gray']) %>% as.character

# We need the entrez ID of the genes for this
getinfo = c('ensembl_gene_id','entrezgene')
mart = useMart(biomart='ENSEMBL_MART_ENSEMBL', dataset='hsapiens_gene_ensembl', 
               host='feb2014.archive.ensembl.org')
biomart_output = getBM(attributes=getinfo, filters=c('ensembl_gene_id'), 
                       values=genes_info$ID[genes_info$Module!='gray'], mart=mart) %>%
                 left_join(genes_info %>% dplyr::select(ID, Module,`gene-score`), by = c('ensembl_gene_id'='ID'))

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>% mutate(term = ifelse(`gene-score` == 'Others', 'Others', 'SFARI'), 
                                      'gene' = entrezgene) %>%  dplyr::select(term, gene) %>% distinct


enrichment_data = data.frame('Module' = modules, 'size' = 0, 'perc_SFARI' = 0,
                             'pval_ORA' = 0, 'padj_ORA' = 0)

for(i in 1:length(modules)){
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 50000) %>% 
                        data.frame %>% dplyr::select(-geneID,-Description)
  ORA_pval = ifelse('SFARI' %in% ORA_module$ID, ORA_module$pvalue[ORA_module$ID=='SFARI'], 1)
  ORA_padj = ifelse('SFARI' %in% ORA_module$ID, ORA_module$p.adjust[ORA_module$ID=='SFARI'], 1)
  enrichment_data[i,-1] = c(length(genes_in_module), 
                            mean(genes_info$`gene-score`[genes_info$Module==module]!='Others'), 
                            ORA_pval, ORA_padj)
}

enrichment_data = enrichment_data %>% 
                  left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')

rm(i, module, genes_in_module, ORA_module, ORA_pval, ORA_padj, getinfo, mart, term2gene)

Note: in ORA, a lower probability indicates a higher enrichment in SFARI Genes, so I’m using 1-probability to measure the enrichment of each module

The two metrics agree quite well, but if we focus on the modules with the highest ‘enrichment’ with both metrics we can see that the smallest modules are below the trend line while the larger ones are above, which shows the bias towards small modules the percentage of SFARI Genes metric has, making the ORA Enrichment metric more desirable

ggplotly(enrichment_data %>% ggplot(aes(perc_SFARI, 1-pval_ORA, size=size)) + 
         geom_point(color = enrichment_data$Module, alpha = 0.5, aes(id=Module)) + 
         geom_smooth(color='gray', se = FALSE) + 
         xlab('% of SFARI Genes') + ylab('ORA Enrichment') + ggtitle('Modules') + theme_minimal())

SFARI Enrichment vs Module-Diagnosis Correlation

There doesn’t seem to be a strong relation between these two metrics, if anything, they seem to contradict each other, mainly in modules with a high Module-Diagnosis correlation, which are the ones with the lowest trend for Enrichment on SFARI Genes (!)

Cor(SFARI Enrichment, Module-Diagnosis) = -0.17

• Correlation for modules with a positive Module-Diagnosis correlation = -0.25

• Correlation for modules with a negative Module-Diagnosis correlation = -0.08

ggplotly(enrichment_data %>% ggplot(aes(MTcor, 1-pval_ORA, size=size)) + 
         geom_point(color=enrichment_data$Module, alpha=0.5, aes(id=Module)) + 
         geom_smooth(color='#cccccc', size = 0.5,alpha=0.1) + xlab('Module-Diagnosis Correlation') + 
         ggtitle('SFARI Enrichment vs Module-Diagnosis Correlation') +
         ylab('Enrichment in SFARI Genes') + theme_minimal() + theme(legend.position = 'none'))

# Save for comparison with old SFARI Genes
enrichment_data_new_SFARI = enrichment_data

Dividing the SFARI Genes by score we get the same pattern, just noisier because the groups are smaller now

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>%
            mutate('term' = ifelse(`gene-score` == 'Others', 'Others', `gene-score`), 
                   'gene' = entrezgene) %>% dplyr::select(term, gene) %>% distinct


enrichment_data_by_score = data.frame('Module' = as.character(), 'size' = as.numeric(), 
                                      'SFARI_score' = as.character(), 'pval_ORA' = as.numeric(), 
                                      'padj_ORA' = as.numeric())

SFARI_scores = SFARI_genes$`gene-score` %>% table %>% names

for(i in 1:length(modules)){
  
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 1e3)
  
  if(length(ORA_module)>0){
    ORA_module = ORA_module %>% data.frame %>% dplyr::select(ID, pvalue, p.adjust) %>%
                 add_column(.before = 'ID', Module = module) %>% 
                 add_column(.before = 'ID', size = length(genes_in_module)) %>%
                 dplyr::rename('SFARI_score' = ID, 'pval_ORA' = pvalue, 'padj_ORA' = p.adjust)
    
    missing_scores = SFARI_scores[!SFARI_scores %in% ORA_module$SFARI_score]
  } else{
    missing_scores = SFARI_scores
  }
  
  if(length(missing_scores)>0){
    for(ms in missing_scores) ORA_module = rbind(ORA_module, c(module, length(genes_in_module), ms, 1, 1))
  }
  
  colnames(ORA_module) = c('Module','size','SFARI_score','pval_ORA','padj_ORA')
  
  enrichment_data_by_score = rbind(enrichment_data_by_score, ORA_module)
}


enrichment_data_by_score = enrichment_data_by_score %>% 
                           left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')


enrichment_data_by_score = enrichment_data_by_score %>% 
                  mutate(color = SFARI_colour_hue(r = 1:3)[SFARI_score %>% as.numeric])

ggplotly(enrichment_data_by_score %>% 
         ggplot(aes(MTcor, 1-as.numeric(pval_ORA), size=size, color = color, fill = color)) + 
         geom_point(alpha=0.5, aes(id=Module)) + geom_smooth(size = 0.5, alpha = 0.1) +
         xlab('Module-Diagnosis Correlation') + ylab('Enrichment') + 
         scale_colour_manual(values = SFARI_colour_hue(r=1:3)) +
         scale_fill_manual(values = SFARI_colour_hue(r=1:3)) + 
         ggtitle('Enrichment by SFARI Gene Score') + 
         theme_minimal() + theme(legend.position = 'none'))

rm(i, module, genes_in_module, ORA_module, term2gene, SFARI_scores, missing_scores, ms, enrichment_data_by_score)

Old SFARI Scores

# SFARI Genes
SFARI_genes = read_csv('./../../../SFARI/Data/SFARI_genes_08-29-2019_w_ensembl_IDs.csv')
SFARI_genes = SFARI_genes[!duplicated(SFARI_genes$ID) & !is.na(SFARI_genes$ID),]

plot_data = plot_data %>% dplyr::select(-gene.score) %>% 
            left_join(SFARI_genes %>% dplyr::select(ID, `gene-score`), by = 'ID') %>%
            mutate(gene.score = ifelse(!is.na(`gene-score`), `gene-score`, 
                                       ifelse(ID %in% GO_neuronal$ID, 'Neuronal', 'Others')))

SFARI Scores vs Gene Significance

• All SFARI Scores have except Score 6 a lower median than all genes that have a neuronal-related annotation (!)

• SFARI Score 1 has a lower median than the non-SFARI non-Neuronal genes (!)

• Neuronal annotated genes have higher Gene Significance than genes without any neuronal-related annotation (makes sense)

• These differences are generally not statistically significant, but it could be because in part because there are very few genes in each of the SFARI scores

comparisons = list(c('1','2'), c('2','3'), c('3','4'), c('4','5'), c('5','6'), c('6','Neuronal'), c('Neuronal','Others'),
                   c('1','3'), c('3','5'), c('5','Neuronal'), 
                   c('2','4'), c('4','6'), c('6','Others'),
                   c('1','4'), c('4','Neuronal'),
                   c('2','5'), c('5','Others'),
                   c('3','Neuronal'), c('1','5'), c('2','6'), c('3','Neuronal'), c('4','Others'))
increase = 0.06
base = 1
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
                      rep(base + 4*increase, 2), base + 5:9*increase)

plot_data %>% ggplot(aes(gene.score, abs(GS), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() + 
              ylab('Gene Significance Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Scores vs Module-Diagnosis correlation

• The highest SFARI scores have a lower Module-Trait correlation (!)

• The group with the highest Module-Diagnosis correlation is SFARI score 6, which is supposed to be the one with the least amount of evidence suggesting a relation to autism (!)

• Most differences are not statistically significant

increase = 0.06
base = 1.1
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
                      rep(base + 4*increase, 2), base + 5:9*increase)

plot_data %>% ggplot(aes(gene.score, abs(MTcor), fill=gene.score)) + 
              geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) + 
              stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test', 
                                 method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, 
                                 tip.length = .01) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() + 
              ylab('Module-Diagnosis Correlation Magnitude') + xlab('SFARI Scores') + theme(legend.position='none')

rm(increase, base, pos_y_comparisons)

SFARI Enrichment vs Module-Diagnosis correlation

Percentage of SFARI Genes vs ORA by Module

# Calculate % and ORA of SFARI Genes in each module

# update biomart_output SFARI labels
biomart_output = biomart_output %>% dplyr::select(-`gene-score`) %>%
                 left_join(plot_data %>% dplyr::select(ID, `gene-score`), by = c('ensembl_gene_id'='ID'))

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>% mutate(term = ifelse(is.na(`gene-score`), 'Others', 'SFARI'), 
                                      'gene' = entrezgene) %>%  dplyr::select(term, gene) %>% distinct


enrichment_data = data.frame('Module' = modules, 'size' = 0, 'perc_SFARI' = 0,
                       'pval_ORA' = 0, 'padj_ORA' = 0)

for(i in 1:length(modules)){
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 50000) %>% 
                        data.frame %>% dplyr::select(-geneID,-Description)
  ORA_pval = ifelse('SFARI' %in% ORA_module$ID, ORA_module$pvalue[ORA_module$ID=='SFARI'], 1)
  ORA_padj = ifelse('SFARI' %in% ORA_module$ID, ORA_module$p.adjust[ORA_module$ID=='SFARI'], 1)
  enrichment_data[i,-1] = c(length(genes_in_module), 
                          mean(!is.na(plot_data$`gene-score`[plot_data$Module==module])), 
                          ORA_pval, ORA_padj)
}

enrichment_data = enrichment_data %>% 
                  left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')

rm(i, module, genes_in_module, ORA_module, ORA_pval, ORA_padj, getinfo, mart, term2gene)

Note: in ORA, a lower probability indicates a higher enrichment in SFARI Genes, so I’m using 1-probability to measure the enrichment of each module

The two metrics agree quite well, but if we focus on the modules with the highest ‘enrichment’ with both metrics we can see that the smallest modules are below the trend line while the larger ones are above, which shows the bias towards small modules the percentage of SFARI Genes metric has, making the ORA Enrichment metric more desirable

ggplotly(enrichment_data %>% ggplot(aes(perc_SFARI, 1-pval_ORA, size=size)) + 
         geom_point(color = enrichment_data$Module, alpha = 0.5, aes(id=Module)) + 
         geom_smooth(color='gray', se = FALSE) + 
         xlab('% of SFARI Genes') + ylab('ORA Enrichment') + ggtitle('Modules') + theme_minimal())

SFARI Enrichment vs Module-Diagnosis Correlation

There is a stronger relation between these two metrics than with the new SFARI Genes:

• As before, modules with a high Module-Diagnosis correlation are the ones with the lowest trend of Enrichment on SFARI Genes(!)

• But this time, there seems to be a positive relation between the magnitude of the Module-Diagnosis correlation and the SFARI Enrichment for the modules with the highest (negative) Module-Trait Diagnosis, which is lost in the new SFARI Genes dataset

Cor(SFARI Enrichment, Module-Diagnosis) = -0.13

• Correlation for modules with a positive Module-Diagnosis correlation = -0.26

• Correlation for modules with a negative Module-Diagnosis correlation = -0.13

ggplotly(enrichment_data %>% ggplot(aes(MTcor, 1-pval_ORA, size=size)) + 
         geom_point(color=enrichment_data$Module, alpha=0.5, aes(id=Module)) + 
         geom_smooth(color='#cccccc', size = 0.5, alpha=0.1) + xlab('Module-Diagnosis Correlation') + 
         ggtitle('SFARI Enrichment vs Module-Diagnosis Correlation') +
         ylab('Enrichment in SFARI Genes') + theme_minimal() + theme(legend.position = 'none'))

Dividing the SFARI Genes by score we get the same pattern, just much noisier because the groups are smaller now. SFARI Score 1 could be enriched in genes with high (positive) Module-Diagnosis correlation, but this pattern also could be just because there are very few genes with a SFARI Score 1, making the results unreliable

# We need to build a term2gene dataframe with the genes and their SFARI Scores
term2gene = biomart_output %>%
            mutate('term' = ifelse(`gene-score` == 'Others', 'Others', `gene-score`), 
                   'gene' = entrezgene) %>% dplyr::select(term, gene) %>% distinct


enrichment_data_by_score = data.frame('Module' = as.character(), 'size' = as.numeric(), 
                                      'SFARI_score' = as.character(), 'pval_ORA' = as.numeric(), 
                                      'padj_ORA' = as.numeric())

SFARI_scores = SFARI_genes$`gene-score` %>% table %>% names

for(i in 1:length(modules)){
  
  module = modules[i]
  genes_in_module = biomart_output$entrezgene[biomart_output$Module==module]
  ORA_module = enricher(gene = genes_in_module, universe = biomart_output$entrezgene %>% as.character, 
                        pAdjustMethod = 'bonferroni', TERM2GENE = term2gene, 
                        pvalueCutoff = 1, qvalueCutoff = 1, maxGSSize = 1e3)
  
  if(length(ORA_module)>0){
    ORA_module = ORA_module %>% data.frame %>% dplyr::select(ID, pvalue, p.adjust) %>%
                 add_column(.before = 'ID', Module = module) %>% 
                 add_column(.before = 'ID', size = length(genes_in_module)) %>%
                 dplyr::rename('SFARI_score' = ID, 'pval_ORA' = pvalue, 'padj_ORA' = p.adjust)
    
    missing_scores = SFARI_scores[!SFARI_scores %in% ORA_module$SFARI_score]
  } else{
    missing_scores = SFARI_scores
  }
  
  if(length(missing_scores)>0){
    for(ms in missing_scores) ORA_module = rbind(ORA_module, c(module, length(genes_in_module), ms, 1, 1))
  }
  
  colnames(ORA_module) = c('Module','size','SFARI_score','pval_ORA','padj_ORA')
  
  enrichment_data_by_score = rbind(enrichment_data_by_score, ORA_module)
}


enrichment_data_by_score = enrichment_data_by_score %>% 
                           left_join(genes_info %>% dplyr::select(Module, MTcor) %>% unique, by = 'Module')


enrichment_data_by_score = enrichment_data_by_score %>% 
                  mutate(color = SFARI_colour_hue(r = 1:6)[SFARI_score %>% as.numeric])

ggplotly(enrichment_data_by_score %>% 
         ggplot(aes(MTcor, 1-as.numeric(pval_ORA), size=size, color = color, fill = color)) + 
         geom_point(alpha=0.5, aes(id=Module)) + geom_smooth(size = 0.5, alpha = 0.1) +
         xlab('Module-Diagnosis Correlation') + ylab('Enrichment') + 
         scale_colour_manual(values = SFARI_colour_hue(r=1:6)) +
         scale_fill_manual(values = SFARI_colour_hue(r=1:6)) + 
         ggtitle('Enrichment by SFARI Gene Score') + 
         theme_minimal() + theme(legend.position = 'none'))

rm(i, module, genes_in_module, ORA_module, term2gene, SFARI_scores, missing_scores, ms, enrichment_data_by_score)

Comparison between Old and New SFARI Genes

• With both SFARI Gene lists, there seems to be a small negative correlation between Mdoule-Trait correlation and SFARI Enrichment, with the genes with a negative Module-Diagnosis correlation having higher SFARI enrichment and genes with positive Module-Diagnosis correlation lower SFARI enrichment. This pattern is a bit stronger in the old SFARI Genes

• In the histogram on the right we can see that the enrichment for the new SFARI Genes is stronger for the new SFARI Genes, with more values closer to the extremes (0 and 1) and less enrichments closer to the middle

compare_plot = enrichment_data %>% dplyr::mutate('Old_SFARI' = pval_ORA) %>% 
               dplyr::select(Module, size, MTcor, Old_SFARI) %>%
               left_join(enrichment_data_new_SFARI %>% dplyr::mutate('New_SFARI' = pval_ORA) %>%
                         dplyr::select(Module, New_SFARI), by = 'Module') %>% 
               melt(id.vars = c('Module','size','MTcor')) %>% dplyr::rename('SFARI_version' = variable) %>%
               mutate(size = sqrt(100*as.numeric(size)/max(as.numeric(size))))

p = compare_plot %>% ggplot(aes(MTcor, 1-as.numeric(value), color = SFARI_version, fill = SFARI_version)) +
    geom_point(alpha = 0.5, size=compare_plot$size, aes(id=Module)) + geom_smooth(alpha = 0.1) + 
    xlab('Module-Diagnosis Correlation') + ylab('Enrichment in SFARI Genes') + 
    ggtitle('SFARI Enrichment vs Module-Diagnosis Correlation') +
    theme_minimal() + theme(legend.position = 'bottom')
          
ggExtra::ggMarginal(p, type = 'density', margins = 'y', groupColour = TRUE, groupFill = TRUE, size=10)

rm(p, compare_plot)

Conclusion:

• Not only are SFARI genes not consistent with the other measurements, but they even seem to contradict them, although the strength of the relations is usually not strong enough to be statistically significant

• Modules with negative Module-Diagnosis correlation have a higher enrichment in SFARI Genes than the genes with a positive Module-Diagnosis correlation (specially the modules with high (positive) correlation, which have the lowest enrichment of all the modules)

• These patterns are visible in both old and new SFARI Scoring systems

Session info

sessionInfo()

## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.4 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
## 
## locale:
##  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8    
##  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8   
##  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] doParallel_1.0.15      iterators_1.0.12       foreach_1.5.0         
##  [4] clusterProfiler_3.12.0 biomaRt_2.40.5         polycor_0.7-10        
##  [7] expss_0.10.2           WGCNA_1.69             fastcluster_1.1.25    
## [10] dynamicTreeCut_1.63-1  ggExtra_0.9            ggpubr_0.2.5          
## [13] magrittr_1.5           GGally_1.5.0           gridExtra_2.3         
## [16] viridis_0.5.1          viridisLite_0.3.0      RColorBrewer_1.1-2    
## [19] dendextend_1.13.4      plotly_4.9.2           glue_1.4.1            
## [22] reshape2_1.4.4         forcats_0.5.0          stringr_1.4.0         
## [25] dplyr_1.0.0            purrr_0.3.4            readr_1.3.1           
## [28] tidyr_1.1.0            tibble_3.0.1           ggplot2_3.3.2         
## [31] tidyverse_1.3.0       
## 
## loaded via a namespace (and not attached):
##   [1] tidyselect_1.1.0            RSQLite_2.2.0              
##   [3] AnnotationDbi_1.46.1        htmlwidgets_1.5.1          
##   [5] grid_3.6.3                  BiocParallel_1.18.1        
##   [7] munsell_0.5.0               codetools_0.2-16           
##   [9] preprocessCore_1.46.0       miniUI_0.1.1.1             
##  [11] withr_2.2.0                 colorspace_1.4-1           
##  [13] GOSemSim_2.10.0             Biobase_2.44.0             
##  [15] knitr_1.28                  rstudioapi_0.11            
##  [17] stats4_3.6.3                ggsignif_0.6.0             
##  [19] DOSE_3.10.2                 labeling_0.3               
##  [21] urltools_1.7.3              GenomeInfoDbData_1.2.1     
##  [23] polyclip_1.10-0             bit64_0.9-7                
##  [25] farver_2.0.3                vctrs_0.3.1                
##  [27] generics_0.0.2              xfun_0.12                  
##  [29] R6_2.4.1                    GenomeInfoDb_1.20.0        
##  [31] graphlayouts_0.7.0          locfit_1.5-9.4             
##  [33] bitops_1.0-6                reshape_0.8.8              
##  [35] fgsea_1.10.1                gridGraphics_0.5-0         
##  [37] DelayedArray_0.10.0         assertthat_0.2.1           
##  [39] promises_1.1.0              scales_1.1.1               
##  [41] ggraph_2.0.3                nnet_7.3-14                
##  [43] enrichplot_1.4.0            gtable_0.3.0               
##  [45] tidygraph_1.2.0             rlang_0.4.6                
##  [47] genefilter_1.66.0           splines_3.6.3              
##  [49] lazyeval_0.2.2              acepack_1.4.1              
##  [51] impute_1.58.0               broom_0.5.5                
##  [53] europepmc_0.4               checkmate_2.0.0            
##  [55] BiocManager_1.30.10         yaml_2.2.1                 
##  [57] modelr_0.1.6                crosstalk_1.1.0.1          
##  [59] backports_1.1.8             httpuv_1.5.2               
##  [61] qvalue_2.16.0               Hmisc_4.4-0                
##  [63] tools_3.6.3                 ggplotify_0.0.5            
##  [65] ellipsis_0.3.1              BiocGenerics_0.30.0        
##  [67] ggridges_0.5.2              Rcpp_1.0.4.6               
##  [69] plyr_1.8.6                  base64enc_0.1-3            
##  [71] progress_1.2.2              zlibbioc_1.30.0            
##  [73] RCurl_1.98-1.2              prettyunits_1.1.1          
##  [75] rpart_4.1-15                cowplot_1.0.0              
##  [77] S4Vectors_0.22.1            SummarizedExperiment_1.14.1
##  [79] haven_2.2.0                 ggrepel_0.8.2              
##  [81] cluster_2.1.0               fs_1.4.0                   
##  [83] data.table_1.12.8           DO.db_2.9                  
##  [85] triebeard_0.3.0             reprex_0.3.0               
##  [87] mvtnorm_1.1-0               matrixStats_0.56.0         
##  [89] hms_0.5.3                   mime_0.9                   
##  [91] evaluate_0.14               xtable_1.8-4               
##  [93] XML_3.99-0.3                jpeg_0.1-8.1               
##  [95] readxl_1.3.1                IRanges_2.18.3             
##  [97] compiler_3.6.3              crayon_1.3.4               
##  [99] htmltools_0.4.0             mgcv_1.8-31                
## [101] later_1.0.0                 Formula_1.2-3              
## [103] geneplotter_1.62.0          lubridate_1.7.4            
## [105] DBI_1.1.0                   tweenr_1.0.1               
## [107] dbplyr_1.4.2                MASS_7.3-51.6              
## [109] Matrix_1.2-18               cli_2.0.2                  
## [111] igraph_1.2.5                GenomicRanges_1.36.1       
## [113] pkgconfig_2.0.3             rvcheck_0.1.8              
## [115] foreign_0.8-76              xml2_1.2.5                 
## [117] annotate_1.62.0             XVector_0.24.0             
## [119] rvest_0.3.5                 digest_0.6.25              
## [121] rmarkdown_2.1               cellranger_1.1.0           
## [123] fastmatch_1.1-0             htmlTable_1.13.3           
## [125] curl_4.3                    shiny_1.4.0.2              
## [127] lifecycle_0.2.0             nlme_3.1-147               
## [129] jsonlite_1.7.0              fansi_0.4.1                
## [131] pillar_1.4.4                lattice_0.20-41            
## [133] fastmap_1.0.1               httr_1.4.1                 
## [135] survival_3.1-12             GO.db_3.8.2                
## [137] UpSetR_1.4.0                png_0.1-7                  
## [139] bit_1.1-15.2                ggforce_0.3.1              
## [141] stringi_1.4.6               blob_1.2.1                 
## [143] DESeq2_1.24.0               latticeExtra_0.6-29        
## [145] memoise_1.1.0